We report focusing of coherent light through opaque scattering materials by control of the incident wavefront. The multiply scattered light forms a focus with a brightness that is up to a factor of 1000 higher than the brightness of the normal diffuse transmission.

We demonstrate experimentally that disordered scattering can be used to improve, rather than deteriorate, the focusing resolution of a lens. By using wavefront shaping to compensate for scattering, light was focused to a spot as small as one tenth of the diffraction limit of the lens. We show both experimentally and theoretically that it is the scattering medium, rather than the lens, that determines the width of the focus. Despite the disordered propagation of the light, the profile of the focus was always exactly equal to the theoretical best focus that we derived.Optical microscopy and manipulation methods rely on the ability to focus light to a small volume. However, in inhomogeneous media, such as biological tissue, light is scattered out of the focusing beam. Disordered scattering is thought to fundamentally limit the resolution and penetration depth of optical methods [1,2,3]. Here we demonstrate in an optical experiment that this very scattering can be exploited to improve, rather than deteriorate, the sharpness of the focus. Surprisingly, the resulting focus is even sharper than in a transparent medium. By using scattering in the medium behind a lens, light was focused to a spot as small as one tenth of the diffraction limit of that lens. Our results, obtained using spatial wavefront shaping, are valid for all methods for focusing coherent light through scattering matter, including phase conjugation [4] and time-reversal [5]. We anticipate that disorder-assisted focusing will improve the imaging resolution of microscopy in inhomogeneous media. The starting situation of the experiment is shown in Fig. 1a: a lens focuses a beam of light onto a CCD camera. In this 'clean' system without disorder, the sharpness of the focus is limited by the numerical aperture and the quality of the lens. We now disturb the light propagation by placing a non-transparent scattering object in the beam path. Although initially the focus disappears, the focus can be restored by shaping the wavefront of the incident light using a spatial light modulator[6] (see Fig. 1b). Here we report and analyze a surprising property of the restored focus: the experimentally obtained focal spot is smaller than the diffraction limit of the clean system. We show both experimentally and theoretically that it is the scattering medium, rather than the lens or the quality of the reconstruction process, that determines the width of the focus. In Fig. 2a we show the measured intensity distribution in the focal plane of the clean system. Ideally, the lens would focus light to an Airy disk with a full width at half maximum (FWHM) of w = 1.03λf 1 /D 1 . In our experiment, λ = 632.8 nm, f 1 = 200 mm, and D 1 = 2.1 mm, FIG. 1: Schematic of the experiment. Light coming from a phase modulator is imaged on the centre plane of a lens, L1 (modulator and imaging telescope not shown). The numerical aperture of the lens is controlled by a pinhole. A CCD camera is positioned in the focal plane of the lens. (a), 'Clean' system without disorder. Light is focused to a...

Light propagation in materials with microscopic inhomogeneities is affected by scattering. In scattering materials, such as powders, disordered metamaterials or biological tissue, multiple scattering on sub-wavelength particles makes light diffuse. Recently, we showed that it is possible to construct a wavefront that focuses through a solid, strongly scattering object. The focusing wavefront uniquely matches a certain configuration of the particles in the medium. To focus light through a turbid liquid or living tissue, it is necessary to dynamically adjust the wavefront as the particles in the medium move. Here we present three algorithms for constructing a wavefront that focuses through a scattering medium. We analyze the dynamic behavior of these algorithms and compare their sensitivity to measurement noise. The algorithms are compared both experimentally and using numerical simulations. The results are in good agreement with an intuitive model, which may be used to develop dynamic diffusion compensators with applications in, for example, light delivery in human tissue.Comment: 28 pages double spaced, 9 figure

We experimentally demonstrate increased diffuse transmission of light through strongly scattering materials. Wave front shaping is used to selectively couple light to the open transport eigenchannels, specific solutions of Maxwell's equations which the sample transmits fully, resulting in an increase of up to 44% in the total angle-integrated transmission compared to the case where plane waves are incident. The results for each of several hundreds of experimental runs are in excellent quantitative agreement with random matrix theory. From our measurements we conclude that with perfectly shaped wave fronts the transmission of a disordered sample tends to a universal value of 2/3, regardless of the thickness.

Light scattering was thought to be the fundamental limitation for the depth at which optical imaging methods can retain their resolution and sensitivity. However, it was shown that light can be focused inside even the most strongly scattering objects by spatially shaping the wavefront of the incident light. This review summarizes recently developed feedback-based approaches for focusing light inside and through scattering objects.